how long will it take C to double population of L

Question

Suppose L = 57 + 1.5t and C = 6 + 4.5t represent the population (in thousands) of two cities, Lanesville and Clarksville, respectively. In how many years will Clarksville have twice as many inhabitants as Lanesville

Answer 1

What you want is for C to be equal to 2 times L, or C = 2L

 

Since you have expressions for C and L, you can substitute those expressions into the above equation:

 

C = 2L

6 + 4.5t = 2(57 + 1.5t)

 

Now you can solve this and see what t comes out to:

 

6 + 4.5t = 2(57 + 1.5t)

6 + 4.5t = 114 + 3t

4.5t = 108 + 3t

1.5t = 108

t = 72

 

The problem, though, is that you don't know what units t is expressed in.  Is it months, years?

 

If t is the number of years, then the answer is 72 years.

 

If t is the number of months, then the answer is 72/12 = 6 years.